An Easy Method To Accelerate An Iterative Algebraic Equation Solver
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
This article proposes to add a simple term to an iterative algebraic equation solver with an order n convergence rate, and to raise the order of convergence to (2n - 1). In particular, a simple algebraic equation solver with the 5th order convergence but uses only 4 function values in each iteration, is described in details. When this scheme is applied to a Newton-Raphson method of the quadratic convergence for a system of algebraic equations, a cubic convergence can be achieved with an low overhead cost of function evaluation that can be ignored as the size of the system increases.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48; AC52-07NA27344
- OSTI ID:
- 1116976
- Report Number(s):
- LLNL-TR-648574
- Country of Publication:
- United States
- Language:
- English
Similar Records
An Easy Method to Accelerate an Iterative Algebraic Solver, part II
On a convergence criterion for linear (inner) iterative solvers for reservoir simulation
Simple Construction of High Order Rational Iterative Equation Solvers
Journal Article
·
Wed Apr 09 00:00:00 EDT 2014
· Proposed Journal Article, unpublished
·
OSTI ID:1116976
On a convergence criterion for linear (inner) iterative solvers for reservoir simulation
Journal Article
·
Fri Feb 01 00:00:00 EST 1985
· Soc. Pet. Eng. AIME, Pap.; (United States)
·
OSTI ID:1116976
Simple Construction of High Order Rational Iterative Equation Solvers
Technical Report
·
Mon Mar 03 00:00:00 EST 2014
·
OSTI ID:1116976